Finite Group Databasebeta

← #14323679

Subgroups — #14323679

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67⋊AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×D3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
3D5×#883C211yesmaximal, characteristic
4#11752358C211yesmaximal, characteristic, complemented
5C3×#65700C211yesmaximal, characteristic, complemented
6#11752055C211yesmaximal, characteristic
7#11752029C211yesmaximal, characteristic, complemented
8#11752018C211yesmaximal, characteristic, complemented
9#11751934C211yesmaximal, characteristic, complemented
10AGL(1,𝔽5)×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11751859C211yesmaximal, characteristic, complemented
12#11751853C211yesmaximal, characteristic, complemented
13#11751845C211yesmaximal, characteristic, complemented
14#11751840C211yesmaximal, characteristic, complemented
15#11751837C211yesmaximal, characteristic, complemented
16#10617304—31nomaximal, Hall
17C23×ΓL(1,𝔽16)C2211yescharacteristic
18C22×D3×AGL(1,𝔽5)C2211yescharacteristic
19C22×D3×AGL(1,𝔽5)C2211yescharacteristic
20C2×D5×#67C2211yescharacteristic
21C2×C4×D3×D5C2211yescharacteristic
22C2×#6763C2211yescharacteristic
23C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
24C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
25C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
26C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
27C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
28C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
29#67⋊AGL(1,𝔽5)—24no—
30C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
31C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
32C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
33C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
34C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
35C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
36C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
37C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
38D3×C4⋊AGL(1,𝔽5)—24no—
39#91772C411yescharacteristic, complemented
40C5×#883C411yescharacteristic, complemented
41C3×D5×C22⋊C4C2211yescharacteristic
42#91562C411yescharacteristic, complemented
43#91555C411yescharacteristic, complemented
44D5×#217C2211yescharacteristic
45D5×(C2×D3)⋊C4C2211yescharacteristic
46#91457C411yescharacteristic, complemented
47#91452C411yescharacteristic, complemented
48D5×C4⋊Dic3C2211yescharacteristic
49D5×Dic3⋊C4C2211yescharacteristic
50#91356C411yescharacteristic, complemented
51#91354C411yescharacteristic, complemented
52#91235C2211yescharacteristic
53#91235C2211yescharacteristic
54C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
55C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
56(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
57(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
58(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
59(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
60(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
61(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
62#75828—51nomaximal, Hall
63C2×D4×AGL(1,𝔽5)—31no—
64C22×C4⋊AGL(1,𝔽5)—31no—
65D5×#123—31no—
66#65779—31no—
67#65764—31no—
68#65712—31no—
69#65712—31no—
70#65711—31no—
71#65711—31no—
72#65700—31no—
73#65700D311yescharacteristic, complemented
74#65699—31no—
75#65699—31no—
76#65699—31no—
77C22⋊C4×AGL(1,𝔽5)—31no—
78C23×C3×D5C2311yescharacteristic
79C22×D3×D5C2311yescharacteristic
80C22×ΓL(1,𝔽16)—22no—
81C22×ΓL(1,𝔽16)—41no—
82C22×ΓL(1,𝔽16)—41no—
83C22×ΓL(1,𝔽16)C2311yescharacteristic
84C22×ΓL(1,𝔽16)C2311yescharacteristic
85C22×ΓL(1,𝔽16)C2311yescharacteristic
86C22×ΓL(1,𝔽16)C2311yescharacteristic
87C22×C3×AGL(1,𝔽5)C2311yescharacteristic
88C22×C3×AGL(1,𝔽5)C2311yescharacteristic
89C22×C3×AGL(1,𝔽5)C2311yescharacteristic
90C22×C3×AGL(1,𝔽5)C2311yescharacteristic
91C2×D3×AGL(1,𝔽5)—22no—
92C2×D3×AGL(1,𝔽5)—41no—
93C2×D3×AGL(1,𝔽5)—41no—
94C2×D3×AGL(1,𝔽5)—41no—
95C2×D3×AGL(1,𝔽5)—41no—
96C2×D3×AGL(1,𝔽5)D414yes—
97C2×#1220C2×C411yescharacteristic
98C2×C4×D15C2×C411yescharacteristic, complemented
99C2×C5×#67C2×C411yescharacteristic
100C2×C4×C5×D3C2×C411yescharacteristic, complemented
101C2×C3×C4×D5C2311yescharacteristic
102C2×C3×C4×D5C2311yescharacteristic
103D5×#67—22no—
104D5×#67—22no—
105C2×#1202C2×C411yescharacteristic
106C2×#1201C2×C411yescharacteristic
107C2×#1200C2×C411yescharacteristic, complemented
108C2×D3×Dic5C2×C411yescharacteristic, complemented
109C2×D5×Dic3C2311yescharacteristic
110C2×D5×Dic3C2311yescharacteristic
111C2×D5×Dic3C2311yescharacteristic
112C4×D3×D5—22no—
113C4×D3×D5—22no—
114#6763—41no—
115C4⋊ΓL(1,𝔽16)—22no—
116C4⋊ΓL(1,𝔽16)—41no—
117C3×C22⋊AGL(1,𝔽5)—22no—
118C3×C22⋊AGL(1,𝔽5)—41no—
119C3×C4⋊AGL(1,𝔽5)—22no—
120C3×C4×AGL(1,𝔽5)—41no—
121Dic3⋊AGL(1,𝔽5)—22no—
122Dic3⋊AGL(1,𝔽5)—22no—
123Dic3⋊AGL(1,𝔽5)—22no—
124Dic3⋊AGL(1,𝔽5)—41no—
125(C2×D3)⋊AGL(1,𝔽5)—22no—
126(C2×D3)⋊AGL(1,𝔽5)—22no—
127Dic3×AGL(1,𝔽5)—22no—
128Dic3×AGL(1,𝔽5)—41no—
129C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
130#6719C2×C411yescharacteristic, complemented
131#6714C2×C411yescharacteristic, complemented
132C4⋊Dic15C2×C411yescharacteristic, complemented
133#6712C2×C411yescharacteristic, complemented
134C5×#217C2×C411yescharacteristic, complemented
135C5×(C2×D3)⋊C4C2×C411yescharacteristic, complemented
136C5×C4⋊Dic3C2×C411yescharacteristic, complemented
137C5×Dic3⋊C4C2×C411yescharacteristic, complemented
138C3×C22⋊Dic5C2×C411yescharacteristic, complemented
139C3×#685C2×C411yescharacteristic, complemented
140C3×#685C2×C411yescharacteristic, complemented
141Dic3⋊Dic5C2×C411yescharacteristic, complemented
142#6669C2×C411yescharacteristic, complemented
143#6668C2×C411yescharacteristic, complemented
144#6668C2×C411yescharacteristic, complemented
145#6667C2×C411yescharacteristic, complemented
146(C2×D3)⋊Dic5C2×C411yescharacteristic, complemented
147#6665C2×C411yescharacteristic, complemented
148#6665C2×C411yescharacteristic, complemented
149C2×D3×C4⋊C4—51no—
150C2×#883—51no—
151C2×#67⋊C4—51no—
152C3×#388—51no—
153#4976—51no—
154#4956—51no—
155#4950—51no—
156#4946—51no—
157#4945—51no—
158C4×(C2×D3)⋊C4—51no—
159#4928—51no—
160#4668—51no—
161#4664—51no—
162#4655—51no—
163#4654—51no—
164C23×AGL(1,𝔽5)—31no—
165C23×AGL(1,𝔽5)—31no—
166C23×AGL(1,𝔽5)—31no—
167C2×D4×D5—31no—
168C22×C4×D5—31no—
169C2×C22⋊AGL(1,𝔽5)—31no—
170C2×C22⋊AGL(1,𝔽5)—31no—
171C2×C22⋊AGL(1,𝔽5)—31no—
172C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
173C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
174D4×AGL(1,𝔽5)—64no—
175C2×C4⋊AGL(1,𝔽5)—31no—
176C2×C4⋊AGL(1,𝔽5)—31no—
177C2×C4⋊AGL(1,𝔽5)—31no—
178C2×C4⋊AGL(1,𝔽5)—31no—
179C2×C4⋊AGL(1,𝔽5)—31no—
180C2×C4⋊AGL(1,𝔽5)—31no—
181C2×C4⋊AGL(1,𝔽5)—64no—
182C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
183C2×C4×AGL(1,𝔽5)—31no—
184C2×C4×AGL(1,𝔽5)—31no—
185C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
186C5×#123—31no—
187#4081—31no—
188#4075—31no—
189#4040—31no—
190#4040—31no—
191D5×C4⋊C4—31no—
192D5×C4⋊C4—31no—
193#4032—31no—
194#4029—31no—
195#4029—31no—
196D5×C22⋊C4—31no—
197D5×C22⋊C4—31no—
198D5×C22⋊C4C2×D311yescharacteristic
199(C2×AGL(1,𝔽5))⋊C4—31no—
200(C2×AGL(1,𝔽5))⋊C4—31no—
201(C2×AGL(1,𝔽5))⋊C4—31no—
202(C2×AGL(1,𝔽5))⋊C4—31no—
203(C2×AGL(1,𝔽5))⋊C4—31no—
204(C2×AGL(1,𝔽5))⋊C4—31no—
205(C2×AGL(1,𝔽5))⋊C4—31no—
206(C2×AGL(1,𝔽5))⋊C4—31no—
207(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
208(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
209#2322—151noSylow
210C23×C3×C5C22×C411yescharacteristic
211C22×D15C22×C411yescharacteristic
212C22×C5×D3C22×C411yescharacteristic
213C22×C3×D5—21no—
214C22×C3×D5—21no—
215C22×C3×D5—21no—
216C22×C3×D5—21no—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5C22×C411yescharacteristic
220C22×C3×D5C2411yescharacteristic
221C2×D3×D5—21no—
222C2×D3×D5—21no—
223C2×D3×D5—21no—
224C2×D3×D5—21no—
225C2×D3×D5C2×D412yes—
226C2×D3×D5#4112yes—
227C2×ΓL(1,𝔽16)—21no—
228C2×ΓL(1,𝔽16)—21no—
229C2×ΓL(1,𝔽16)—21no—
230C2×ΓL(1,𝔽16)—21no—
231C2×ΓL(1,𝔽16)—21no—
232C2×ΓL(1,𝔽16)—21no—
233C2×ΓL(1,𝔽16)—21no—
234C2×ΓL(1,𝔽16)—21no—
235C2×ΓL(1,𝔽16)—21no—
236C2×ΓL(1,𝔽16)—21no—
237C2×ΓL(1,𝔽16)—21no—
238C2×ΓL(1,𝔽16)—44no—
239C2×ΓL(1,𝔽16)C2×D412yes—
240C2×C3×AGL(1,𝔽5)—21no—
241C2×C3×AGL(1,𝔽5)—21no—
242C2×C3×AGL(1,𝔽5)—21no—
243C2×C3×AGL(1,𝔽5)—21no—
244C2×C3×AGL(1,𝔽5)—21no—
245C2×C3×AGL(1,𝔽5)—21no—
246C2×C3×AGL(1,𝔽5)—21no—
247C2×C3×AGL(1,𝔽5)—21no—
248C2×C3×AGL(1,𝔽5)—21no—
249C2×C3×AGL(1,𝔽5)—21no—
250C2×C3×AGL(1,𝔽5)—21no—
251C2×C3×AGL(1,𝔽5)C2×D412yes—
252D3×AGL(1,𝔽5)—44no—
253D3×AGL(1,𝔽5)—44no—
254C2×C3×C4×C5C22×C411yescharacteristic
255C2×C3×C4×C5C22×C411yescharacteristic
256#1220—22no—
257C2×Dic15C22×C411yescharacteristic
258C2×Dic15C22×C411yescharacteristic
259C2×Dic15C22×C411yescharacteristic
260C4×D15—22no—
261C5×#67—22no—
262C2×C5×Dic3C22×C411yescharacteristic
263C2×C5×Dic3C22×C411yescharacteristic
264C2×C5×Dic3C22×C411yescharacteristic
265C4×C5×D3—22no—
266C2×C3×Dic5C22×C411yescharacteristic
267C2×C3×Dic5C22×C411yescharacteristic
268C3×C4×D5—21no—
269C3×C4×D5—21no—
270C3×C4×D5—21no—
271C3×C4×D5—21no—
272#1202—22no—
273#1201—22no—
274#1200—22no—
275D3×Dic5—22no—
276D5×Dic3—21no—
277D5×Dic3—21no—
278D5×Dic3—21no—
279D5×Dic3—21no—
280D5×Dic3—21no—
281D5×Dic3—21no—
282C22×#67—51no—
283C23×Dic3—51no—
284C22×C4×D3—51no—
285C22×C4×D3—51no—
286C22×C4×D3—51no—
287C2×C3×C4⋊C4—51no—
288C2×C3×C22⋊C4—51no—
289C2×C3×C22⋊C4—51no—
290C2×C3×C22⋊C4—51no—
291C2×C3×C42—51no—
292C2×#217—51no—
293C2×#217—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×(C2×D3)⋊C4—51no—
296C2×(C2×D3)⋊C4—51no—
297C2×C4⋊Dic3—51no—
298C2×C4⋊Dic3—51no—
299C2×C4⋊Dic3—51no—
300C2×Dic3⋊C4—51no—
301C2×Dic3⋊C4—51no—
302C2×Dic3⋊C4—51no—
303C2×Dic3⋊C4—51no—
304C2×Dic3⋊C4—51no—
305C2×C4×Dic3—51no—
306C2×C4×Dic3—51no—
307D3×C4⋊C4—104no—
308#883—51no—
309#883—51no—
310#883—51no—
311#883—51no—
312#883—51no—
313#883—51no—
314#883—51no—
315#883AGL(1,𝔽5)11yescharacteristic, complemented
316#67⋊C4—104no—
317C3×#95—51no—
318C3×#95—51no—
319C3⋊#95—51no—
320C3⋊#95—51no—
321C3⋊#95—51no—
322C3⋊#95—51no—
323C3⋊#95—51no—
324C3⋊#95—51no—
325C3⋊#95—51no—
326C3⋊#95—51no—
327C23×D5—31no—
328C23×D5C22×D311yescharacteristic
329C22×AGL(1,𝔽5)—31no—
330C22×AGL(1,𝔽5)—34no—
331C22×AGL(1,𝔽5)—31no—
332C22×AGL(1,𝔽5)—31no—
333C22×AGL(1,𝔽5)—31no—
334C22×AGL(1,𝔽5)—62no—
335C22×AGL(1,𝔽5)—62no—
336C22×AGL(1,𝔽5)—121no—
337C22×AGL(1,𝔽5)—121no—
338C22×AGL(1,𝔽5)—121no—
339C22×AGL(1,𝔽5)—121no—
340C22×AGL(1,𝔽5)—121no—
341C22×AGL(1,𝔽5)—121no—
342C22×AGL(1,𝔽5)C22×D311yescharacteristic
343C22×AGL(1,𝔽5)C22×D311yescharacteristic
344C22×AGL(1,𝔽5)C22×D311yescharacteristic
345C22×AGL(1,𝔽5)C22×D311yescharacteristic
346C2×C5×D4—31no—
347C22×C4×C5—31no—
348C2×C22⋊D5—31no—
349C2×C22⋊D5—31no—
350C22×Dic5—31no—
351D4×D5—62no—
352D4×D5—62no—
353C2×D20—31no—
354C2×C4×D5—31no—
355C2×C4×D5—31no—
356C2×C4×D5—31no—
357C2×C4×D5—31no—
358C2×C4×D5—31no—
359C2×C4×D5—62no—
360C2×C4×D5—62no—
361C2×C4×D5C22×D311yescharacteristic
362C2×C4×D5C22×D311yescharacteristic
363C22⋊AGL(1,𝔽5)—22no—
364C22⋊AGL(1,𝔽5)—41no—
365C22⋊AGL(1,𝔽5)—62no—
366C22⋊AGL(1,𝔽5)—62no—
367C22⋊AGL(1,𝔽5)—121no—
368C4⋊AGL(1,𝔽5)—22no—
369C4⋊AGL(1,𝔽5)—62no—
370C4⋊AGL(1,𝔽5)—62no—
371C4⋊AGL(1,𝔽5)—62no—
372C4⋊AGL(1,𝔽5)—62no—
373C4⋊AGL(1,𝔽5)—121no—
374C4⋊AGL(1,𝔽5)—121no—
375C4×AGL(1,𝔽5)—41no—
376C4×AGL(1,𝔽5)—62no—
377C4×AGL(1,𝔽5)—121no—
378C5×C4⋊C4—31no—
379C5×C4⋊C4—31no—
380C5×C22⋊C4—31no—
381C5×C22⋊C4—31no—
382C5×C22⋊C4C4×D311yescharacteristic, complemented
383C22⋊Dic5—31no—
384C22⋊Dic5—31no—
385C22⋊Dic5C4×D311yescharacteristic, complemented
386#685—31no—
387#685—31no—
388#685—31no—
389#685—31no—
390#685C4×D311yescharacteristic, complemented
391#685C4×D311yescharacteristic, complemented
392C4⋊Dic5—31no—
393C4⋊Dic5—31no—
394#683—31no—
395#683—31no—
396#683—31no—
397#683—31no—
398C2×#123—151no—
399C2×C4×D4—151no—
400C22×C4⋊C4—151no—
401#389—151no—
402#389—151no—
403#388—51no—
404#388—151no—
405#387—151no—
406#387—151no—
407#386—151no—
408#385—151no—
409#385—151no—
410#385—151no—
411#381—151no—
412C4×C22⋊C4—151no—
413C22×C3×C5—21no—
414C22×C3×C5—21no—
415C22×C3×C5—21no—
416C22×C3×C5C23×C411yescharacteristic
417C2×D15—21no—
418C2×D15—21no—
419C2×D15C4×D412yes—
420C2×C5×D3—21no—
421C2×C5×D3—21no—
422C2×C5×D3C4×D412yes—
423C2×C3×D5—21no—
424C2×C3×D5—21no—
425C2×C3×D5—21no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428C2×C3×D5—41no—
429C2×C3×D5—41no—
430C2×C3×D5C22×D411yescharacteristic
431C2×C3×D5C2×#4111yescharacteristic
432C2×C3×D5H(5,𝔽2)11yescharacteristic
433C2×C3×D5H(5,𝔽2)11yescharacteristic
434C2×C3×D52−1+411yescharacteristic
435C2×C3×D52−1+411yescharacteristic
436D3×D5—22no—
437D3×D5—22no—
438D3×D5—22no—
439D3×D5—22no—
440ΓL(1,𝔽16)—22no—
441ΓL(1,𝔽16)—41no—
442ΓL(1,𝔽16)—41no—
443ΓL(1,𝔽16)—41no—
444C3×AGL(1,𝔽5)—22no—
445C3×AGL(1,𝔽5)—41no—
446C3×AGL(1,𝔽5)—41no—
447C3×AGL(1,𝔽5)—41no—
448C3×C4×C5—21no—
449C3×C4×C5—21no—
450Dic15—21no—
451Dic15—21no—
452Dic15—21no—
453C3×Dic5—21no—
454C3×Dic5—21no—
455C5×Dic3—21no—
456C5×Dic3—21no—
457C5×Dic3—21no—
458C24×C3—51no—
459C23×D3—51no—
460C22×C3×C4—51no—
461C22×C3×C4—51no—
462C22×C3×C4—51no—
463C22×C3×C4—51no—
464C22×C3×C4—51no—
465C22×C3×C4—51no—
466C2×#67—51no—
467C2×#67—51no—
468C2×#67—51no—
469C2×#67—102no—
470C2×#67—102no—
471C2×#67C2×AGL(1,𝔽5)11yescharacteristic
472C22×Dic3—51no—
473C22×Dic3—51no—
474C22×Dic3—51no—
475C22×Dic3—51no—
476C22×Dic3—51no—
477C22×Dic3—51no—
478C22×Dic3—51no—
479C22×Dic3—102no—
480C22×Dic3—201no—
481C22×Dic3—201no—
482C2×C4×D3—51no—
483C2×C4×D3—51no—
484C2×C4×D3—51no—
485C2×C4×D3—54no—
486C2×C4×D3—102no—
487C2×C4×D3—102no—
488C2×C4×D3—102no—
489C2×C4×D3—201no—
490C2×C4×D3—201no—
491C2×C4×D3—201no—
492C2×C4×D3—201no—
493C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
494C3×C4⋊C4—102no—
495C3×C22⋊C4—51no—
496C3×C22⋊C4—51no—
497C3×C22⋊C4—51no—
498C3×C22⋊C4—102no—
499C3×C22⋊C4—201no—
500C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
501C3×C42—201no—
502#217—51no—
503#217—51no—
504#217—51no—
505#217—201no—
506#217C2×AGL(1,𝔽5)11yescharacteristic, complemented
507(C2×D3)⋊C4—51no—
508(C2×D3)⋊C4—51no—
509(C2×D3)⋊C4—51no—
510(C2×D3)⋊C4—102no—
511(C2×D3)⋊C4—102no—
512(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
513C4⋊Dic3—51no—
514C4⋊Dic3—51no—
515C4⋊Dic3—51no—
516C4⋊Dic3—102no—
517C4⋊Dic3—201no—
518C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
519Dic3⋊C4—51no—
520Dic3⋊C4—51no—
521Dic3⋊C4—51no—
522Dic3⋊C4—102no—
523Dic3⋊C4—102no—
524Dic3⋊C4—102no—
525Dic3⋊C4—201no—
526Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
527C4×Dic3—102no—
528C4×Dic3—201no—
529C23×C5—31no—
530C23×C5C2×C4×D311yescharacteristic
531C22×D5—21no—
532C22×D5—21no—
533C22×D5—21no—
534C22×D5—21no—
535C22×D5—21no—
536C22×D5—21no—
537C22×D5—31no—
538C22×D5—32no—
539C22×D5—32no—
540C22×D5—61no—
541C22×D5—61no—
542C22×D5—61no—
543C22×D5—61no—
544C22×D5C2×C4×D311yescharacteristic
545C22×D5C23×D311yescharacteristic
546C2×AGL(1,𝔽5)—21no—
547C2×AGL(1,𝔽5)—21no—
548C2×AGL(1,𝔽5)—21no—
549C2×AGL(1,𝔽5)—21no—
550C2×AGL(1,𝔽5)—21no—
551C2×AGL(1,𝔽5)—21no—
552C2×AGL(1,𝔽5)—21no—
553C2×AGL(1,𝔽5)—21no—
554C2×AGL(1,𝔽5)—21no—
555C2×AGL(1,𝔽5)—21no—
556C2×AGL(1,𝔽5)—21no—
557C2×AGL(1,𝔽5)—32no—
558C2×AGL(1,𝔽5)—61no—
559C2×AGL(1,𝔽5)—61no—
560C2×AGL(1,𝔽5)—61no—
561C2×AGL(1,𝔽5)—61no—
562C2×AGL(1,𝔽5)—61no—
563C2×AGL(1,𝔽5)—61no—
564C2×AGL(1,𝔽5)—61no—
565C2×AGL(1,𝔽5)—61no—
566C2×AGL(1,𝔽5)—61no—
567C2×AGL(1,𝔽5)—61no—
568C2×AGL(1,𝔽5)—61no—
569C2×AGL(1,𝔽5)—124no—
570C2×AGL(1,𝔽5)—124no—
571C2×AGL(1,𝔽5)—124no—
572C2×AGL(1,𝔽5)D3×D412yes—
573C5×D4—62no—
574C2×C4×C5—31no—
575C2×C4×C5—31no—
576C2×C4×C5—31no—
577C2×C4×C5—62no—
578C2×C4×C5C2×C4×D311yescharacteristic
579C2×C4×C5C2×C4×D311yescharacteristic
580C22⋊D5—62no—
581C22⋊D5—62no—
582C2×Dic5—31no—
583C2×Dic5—31no—
584C2×Dic5—31no—
585C2×Dic5—62no—
586C2×Dic5C2×C4×D311yescharacteristic
587C2×Dic5C2×C4×D311yescharacteristic
588D20—62no—
589C4×D5—21no—
590C4×D5—21no—
591C4×D5—21no—
592C4×D5—21no—
593C4×D5—62no—
594C4×D5—62no—
595C4×D5—61no—
596C4×D5—61no—
597C4×D5—61no—
598C4×D5—61no—
599C4×D5—61no—
600C4×D5—61no—
601C22×D4—151no—
602C23×C4—151no—
603C23×C4—151no—
604C23×C4—151no—
605C23×C4—151no—
606#123—31no—
607#123—151no—
608#123—151no—
609#123—151no—
610#123—151no—
611#123—151no—
612#123—151no—
613#123—151no—
614C4×D4—304no—
615C2×C4⋊C4—51no—
616C2×C4⋊C4—151no—
617C2×C4⋊C4—151no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4—151no—
621C2×C4⋊C4—151no—
622C2×C4⋊C4—151no—
623C2×C4⋊C4—151no—
624C2×C4⋊C4—304no—
625C2×C22⋊C4—51no—
626C2×C22⋊C4—51no—
627C2×C22⋊C4—51no—
628C2×C22⋊C4—151no—
629C2×C22⋊C4—151no—
630C2×C22⋊C4—151no—
631C2×C22⋊C4—151no—
632C2×C22⋊C4—151no—
633C2×C42—51no—
634C2×C42—151no—
635C2×C42—151no—
636#95—51no—
637#95—51no—
638#95—151no—
639#95—151no—
640#95—151no—
641#95—151no—
642#95—151no—
643#95—151no—
644#95—151no—
645#95—151no—
646C2×C3×C5—41no—
647C2×C3×C5C2×C4×D411yescharacteristic
648C2×C3×C5#52011yescharacteristic
649C2×C3×C5#52011yescharacteristic
650D15—22no—
651C3×D5—41no—
652C3×D5#53411yescharacteristic
653C3×D5#53611yescharacteristic
654C3×D5#53911yescharacteristic
655C3×D5#53911yescharacteristic
656C5×D3—22no—
657C23×C3—51no—
658C23×C3—51no—
659C23×C3—101no—
660C23×C3—101no—
661C23×C3—101no—
662C23×C3—101no—
663C23×C3—101no—
664C23×C3—101no—
665C23×C3C22×AGL(1,𝔽5)11yescharacteristic
666C22×D3—51no—
667C22×D3—52no—
668C22×D3—52no—
669C22×D3—101no—
670C22×D3—101no—
671C22×D3—101no—
672C22×D3—101no—
673C22×D3C22×AGL(1,𝔽5)11yescharacteristic
674C2×C3×C4—52no—
675C2×C3×C4—51no—
676C2×C3×C4—51no—
677C2×C3×C4—101no—
678C2×C3×C4—101no—
679C2×C3×C4—101no—
680C2×C3×C4—101no—
681C2×C3×C4—101no—
682C2×C3×C4—101no—
683C2×C3×C4—101no—
684C2×C3×C4—101no—
685C2×C3×C4—101no—
686C2×C3×C4—101no—
687C2×C3×C4—101no—
688C2×C3×C4—101no—
689C2×C3×C4—101no—
690C2×C3×C4—101no—
691C2×C3×C4—101no—
692C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
693C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
694#67—22no—
695#67—102no—
696#67—102no—
697#67—102no—
698C2×Dic3—52no—
699C2×Dic3—51no—
700C2×Dic3—51no—
701C2×Dic3—51no—
702C2×Dic3—101no—
703C2×Dic3—101no—
704C2×Dic3—101no—
705C2×Dic3—101no—
706C2×Dic3—101no—
707C2×Dic3—101no—
708C2×Dic3—101no—
709C2×Dic3—101no—
710C2×Dic3—101no—
711C2×Dic3—101no—
712C2×Dic3—101no—
713C2×Dic3—101no—
714C2×Dic3—101no—
715C2×Dic3—101no—
716C2×Dic3—101no—
717C2×Dic3—101no—
718C2×Dic3—101no—
719C2×Dic3—204no—
720C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
721C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
722C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
723C4×D3—22no—
724C4×D3—102no—
725C4×D3—102no—
726C4×D3—102no—
727C4×D3—204no—
728C4×D3—204no—
729C22×C5—21no—
730C22×C5—21no—
731C22×C5—21no—
732C22×C5—32no—
733C22×C5—61no—
734C22×C5—61no—
735C22×C5C22×C4×D311yescharacteristic
736C2×D5—21no—
737C2×D5—21no—
738C2×D5—21no—
739C2×D5—32no—
740C2×D5—41no—
741C2×D5—41no—
742C2×D5—41no—
743C2×D5—41no—
744C2×D5—61no—
745C2×D5—61no—
746C2×D5—62no—
747C2×D5—62no—
748C2×D5—62no—
749C2×D5—62no—
750C2×D5C2×D3×D411yescharacteristic
751C2×D5#100411yescharacteristic
752C2×D5D3×#4111yescharacteristic
753C2×D5#100911yescharacteristic
754C2×D5#101011yescharacteristic
755C2×D5#101011yescharacteristic
756AGL(1,𝔽5)—22no—
757AGL(1,𝔽5)—41no—
758AGL(1,𝔽5)—41no—
759AGL(1,𝔽5)—41no—
760AGL(1,𝔽5)—62no—
761AGL(1,𝔽5)—121no—
762AGL(1,𝔽5)—121no—
763AGL(1,𝔽5)—121no—
764C4×C5—21no—
765C4×C5—21no—
766C4×C5—61no—
767C4×C5—61no—
768C4×C5—61no—
769Dic5—21no—
770Dic5—21no—
771Dic5—61no—
772Dic5—61no—
773Dic5—61no—
774C24—51no—
775C24—151no—
776C2×D4—31no—
777C2×D4—151no—
778C2×D4—151no—
779C2×D4—151no—
780C2×D4—302no—
781C2×D4—302no—
782C22×C4—31no—
783C22×C4—51no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—51no—
787C22×C4—51no—
788C22×C4—51no—
789C22×C4—151no—
790C22×C4—151no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4—154no—
795C22×C4—151no—
796C22×C4—151no—
797C22×C4—151no—
798C22×C4—151no—
799C22×C4—151no—
800C22×C4—302no—
801C22×C4—302no—
802C22×C4—302no—
803C22×C4—302no—
804C22×C4—601no—
805C22×C4—601no—
806C22×C4—601no—
807C22×C4—601no—
808C22×C4—601no—
809C22×C4—601no—
810C4⋊C4—31no—
811C4⋊C4—31no—
812C4⋊C4—102no—
813C4⋊C4—151no—
814C4⋊C4—151no—
815C4⋊C4—151no—
816C4⋊C4—151no—
817C4⋊C4—151no—
818C4⋊C4—151no—
819C4⋊C4—302no—
820C4⋊C4—302no—
821C4⋊C4—302no—
822C4⋊C4—302no—
823C4⋊C4—601no—
824C4⋊C4—601no—
825C22⋊C4—31no—
826C22⋊C4—31no—
827C22⋊C4—51no—
828C22⋊C4—51no—
829C22⋊C4—51no—
830C22⋊C4—102no—
831C22⋊C4—151no—
832C22⋊C4—151no—
833C22⋊C4—151no—
834C22⋊C4—151no—
835C22⋊C4—151no—
836C22⋊C4—151no—
837C22⋊C4—201no—
838C22⋊C4—302no—
839C22⋊C4—302no—
840C22⋊C4—601no—
841C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
842C42—201no—
843C42—302no—
844C42—601no—
845C3×C5#232211yescharacteristic, complemented, Hall
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—51no—
850C22×C3—51no—
851C22×C3—51no—
852C22×C3—51no—
853C22×C3—51no—
854C22×C3—51no—
855C22×C3—101no—
856C22×C3—101no—
857C22×C3—101no—
858C22×C3—201no—
859C22×C3—201no—
860C22×C3—201no—
861C22×C3—201no—
862C22×C3C23×AGL(1,𝔽5)11yescharacteristic
863C2×D3—21no—
864C2×D3—21no—
865C2×D3—52no—
866C2×D3—102no—
867C2×D3—102no—
868C2×D3—102no—
869C2×D3—102no—
870C2×D3—101no—
871C2×D3—101no—
872C2×D3D4×AGL(1,𝔽5)12yes—
873C3×C4—21no—
874C3×C4—21no—
875C3×C4—102no—
876C3×C4—101no—
877C3×C4—101no—
878C3×C4—201no—
879C3×C4—201no—
880C3×C4—201no—
881Dic3—21no—
882Dic3—21no—
883Dic3—21no—
884Dic3—102no—
885Dic3—101no—
886Dic3—101no—
887Dic3—101no—
888Dic3—201no—
889Dic3—201no—
890Dic3—201no—
891C2×C5—41no—
892C2×C5—62no—
893C2×C5#552311yescharacteristic
894C2×C5C4×D3×D411yescharacteristic
895C2×C5#554611yescharacteristic
896D5—41no—
897D5—62no—
898D5#560511yescharacteristic
899D5#566011yescharacteristic
900D5#567511yescharacteristic
901D5#570711yescharacteristic
902C23—31no—
903C23—51no—
904C23—51no—
905C23—101no—
906C23—101no—
907C23—101no—
908C23—101no—
909C23—101no—
910C23—101no—
911C23—152no—
912C23—152no—
913C23—151no—
914C23—301no—
915C23—301no—
916C23—301no—
917C23—301no—
918C23C2×D3×AGL(1,𝔽5)11yescharacteristic
919D4—62no—
920D4—302no—
921D4—302no—
922D4—302no—
923C2×C4—31no—
924C2×C4—31no—
925C2×C4—31no—
926C2×C4—52no—
927C2×C4—51no—
928C2×C4—51no—
929C2×C4—62no—
930C2×C4—101no—
931C2×C4—101no—
932C2×C4—101no—
933C2×C4—101no—
934C2×C4—101no—
935C2×C4—101no—
936C2×C4—101no—
937C2×C4—101no—
938C2×C4—101no—
939C2×C4—101no—
940C2×C4—101no—
941C2×C4—101no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—101no—
945C2×C4—152no—
946C2×C4—151no—
947C2×C4—151no—
948C2×C4—151no—
949C2×C4—302no—
950C2×C4—302no—
951C2×C4—301no—
952C2×C4—301no—
953C2×C4—301no—
954C2×C4—301no—
955C2×C4—301no—
956C2×C4—301no—
957C2×C4—302no—
958C2×C4—301no—
959C2×C4—301no—
960C2×C4—301no—
961C2×C4—301no—
962C2×C4—301no—
963C2×C4—301no—
964C2×C4—301no—
965C2×C4—301no—
966C2×C4—301no—
967C2×C4—301no—
968C2×C4—301no—
969C2×C4—604no—
970C2×C4—604no—
971C2×C4—604no—
972C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
973C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
974C2×C3—41no—
975C2×C3—51no—
976C2×C3—51no—
977C2×C3—51no—
978C2×C3—51no—
979C2×C3—201no—
980C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
981C2×C3#6626611yescharacteristic
982C2×C3#6626611yescharacteristic
983D3—22no—
984D3—102no—
985C5#7582811yescharacteristic, complemented, Sylow
986C22—21no—
987C22—21no—
988C22—21no—
989C22—32no—
990C22—51no—
991C22—51no—
992C22—51no—
993C22—51no—
994C22—51no—
995C22—51no—
996C22—61no—
997C22—61no—
998C22—101no—
999C22—101no—
1000C22—101no—
1001C22—152no—
1002C22—201no—
1003C22—201no—
1004C22—201no—
1005C22—201no—
1006C22—302no—
1007C22—302no—
1008C22—302no—
1009C22—302no—
1010C22—301no—
1011C22—301no—
1012C22C22×D3×AGL(1,𝔽5)11yescharacteristic
1013C4—21no—
1014C4—21no—
1015C4—61no—
1016C4—61no—
1017C4—61no—
1018C4—102no—
1019C4—101no—
1020C4—101no—
1021C4—201no—
1022C4—201no—
1023C4—201no—
1024C4—302no—
1025C4—301no—
1026C4—301no—
1027C4—301no—
1028C4—601no—
1029C4—601no—
1030C4—601no—
1031C3#1061730411yescharacteristic, complemented, Sylow
1032C2—41no—
1033C2—51no—
1034C2—51no—
1035C2—51no—
1036C2—51no—
1037C2—62no—
1038C2—201no—
1039C2—302no—
1040C2#1175683811yescharacteristic
1041C2D3×D4×AGL(1,𝔽5)11yescharacteristic
1042C2#1175684611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C4C2×C4
prime radicalC2×D5×#67C22
cosocleC22×C3×D5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#2322
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×D3×C4⋊AGL(1,𝔽5)C2semidirect
4. #11752358C2semidirect
5. C3×#65700C2semidirect
7. #11752029C2semidirect
8. #11752018C2semidirect
9. #11751934C2semidirect
10. AGL(1,𝔽5)×(C2×D3)⋊C4C2semidirect
11. #11751859C2semidirect
12. #11751853C2semidirect
13. #11751845C2semidirect
14. #11751840C2semidirect
15. #11751837C2semidirect
39. #91772C4semidirect
40. C5×#883C4semidirect
42. #91562C4semidirect
43. #91555C4semidirect
46. #91457C4semidirect
47. #91452C4semidirect
50. #91356C4semidirect
51. #91354C4semidirect
73. #65700D3semidirect
98. C2×C4×D15C2×C4semidirect
100. C2×C4×C5×D3C2×C4semidirect
107. C2×#1200C2×C4semidirect
108. C2×D3×Dic5C2×C4semidirect
129. C3×C5×C22⋊C4C2×C4semidirect
130. #6719C2×C4semidirect
131. #6714C2×C4semidirect
132. C4⋊Dic15C2×C4semidirect
133. #6712C2×C4semidirect
134. C5×#217C2×C4semidirect
135. C5×(C2×D3)⋊C4C2×C4semidirect
136. C5×C4⋊Dic3C2×C4semidirect
137. C5×Dic3⋊C4C2×C4semidirect
138. C3×C22⋊Dic5C2×C4semidirect
139. C3×#685C2×C4semidirect
140. C3×#685C2×C4semidirect
141. Dic3⋊Dic5C2×C4semidirect
142. #6669C2×C4semidirect
143. #6668C2×C4semidirect
144. #6668C2×C4semidirect
145. #6667C2×C4semidirect
146. (C2×D3)⋊Dic5C2×C4semidirect
147. #6665C2×C4semidirect
148. #6665C2×C4semidirect
315. #883AGL(1,𝔽5)semidirect
382. C5×C22⋊C4C4×D3semidirect
385. C22⋊Dic5C4×D3semidirect
390. #685C4×D3semidirect
391. #685C4×D3semidirect
493. C2×C4×D3C2×AGL(1,𝔽5)semidirect
500. C3×C22⋊C4C2×AGL(1,𝔽5)semidirect
506. #217C2×AGL(1,𝔽5)semidirect
512. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
518. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
526. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
841. C22⋊C4D3×AGL(1,𝔽5)semidirect
845. C3×C5#2322semidirect
985. C5#75828semidirect
1031. C3#10617304semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#67⋊AGL(1,𝔽5)2
C2×D3×C4⋊AGL(1,𝔽5)2
D5×#8832
#117523582
C3×#657002
#117520552
#117520292
#117520182
#117519342
AGL(1,𝔽5)×(C2×D3)⋊C42
#117518592
#117518532
#117518452
#117518402
#117518372
#106173043
#758285